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In this paper has been considered probability-one global convergence of NFPH(Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations andhas been proposed a probability-one homotopy algorithm to solve a regularizedsmoothing equation for NCP with generalized monotonicity. Our results provide atheoretical basis to develop a new computational method for nonlinear equationsystems and complementarity problems. Some preliminary numerical experimentsshows that our NFPH method is useful and promissing for difficult nonlinearproblems.

A Newton-Fixed Point Homotopy Algorithm For Nonlinear Complementarity Problems With Generalized Monotonicity